Lecture 10 : Whole genome sequencing and analysis Introduction to Computational

Biology Teresa Przytycka, PhD

Sequencing DNA •  Goal – obtain the string of bases that make a given

DNA strand. •  Problem –Typically one cans sequence directly

only DNA of short length (400-700 bp – Sanger; <200 - Illumina).

•  Sequence assembly – the process of putting together the fragments.

Cutting and breaking DNA •  Restriction enzymes – proteins that catalyze hydrolysis

(breaking the molecule by adding water) of DNA at certain points called restriction sides.

•  Example: EcoRI restriction side GAATTC. Note that the complement of GAATTC is GAATTC (a sequence equal to its reverse is called a palindrome)

…ATCCAGAATTCTC… …TAGGTCTTAAGAG

ATCCAG AATTCTC…

…TAGGTCTTAA AG

Fragment assembly

•  After DNA fragments (reads) are sequenced we want to assemble then together to reconstruct the entire target sequence.

•  If the overlaps were unique and error free, this would be relatively easy task… but they are not.

•  In addition : fragments can come from any of the two DNA strands and we do not know which

The “ideal” example

Input: ACCGT CGTGC TTAC TACCGT Assume target sequence of about 10bp. - - ACCGT - - - - CGTGC TTAC - - - - - - TACCGT - - TTACCGTGC consensus sequence

Sample overlaps

Fragment assembly

•  After DNA fragments (reads) are sequenced we want to assemble then together to reconstruct the entire target sequence.

•  Most fragment assembly algorithms include the following 3 steps: –  Overlap - finding potentially overlapping fragments –  Layout – finding the order of the fragments –  Consensus – deriving DNA sequence from the layout.

•  Usually we know with some approximation the length of the target sequence.

Finding overlaps

•  In theory we should test for overlaps all pairs of fragments. For every pair we will consider all relative orientations.

•  One possible method: perform alignment without charging for flanking gaps

- - TAATG TGTAA - -

Representing overlaps F - fragments. Overlap graph : vertices = elements of F weighted edges: if a, b ∈ F then the weight of

edge from a to b is equal t where maximum integer such that

suffix(a,t) = prefix(b,t) suffix(a,t) = last t symbols of a prefix(b,t) = first t symbols of b

Path dbc leads to alignment

Path abcd leads to alignment

a

b

d

c

Each simple path (simple = not using the same vertex more than once) in overlap graph defines an alignment. Two assumptions: - no fragment completely included in another - Direction of fragments is known

Finding Layout

Definition: Hamiltonian path – a path that visits each vertex exactly once.

Let P – path, A the set of fragments involved in A |S(P)| = ||A|| - w(P) Where ||A|| sum of lengths of fragments in

A w(P) the sum of weight of path P (sum of

the edge weights on this paths).

The greedy algorithm

•  Goal: find a Hamiltonian path with large w(P).

•  Heuristic: iteratively find the heavies edge and try to add it to the path:

•  Acceptance test: An edge can be added to the path, if it will not create brunching point on the path.

Algorithm Greedy: sort edges by weight for each edge (f,g) in decreasing order

perform acceptance test for (f,g) if accepted add it to the path

Example: greedy choice Try: (a,d) – ok, selected Try: (d,b) – ok, selected Try: (a,b) – acceptance test false Try: (b,c) – ok, selected

a

b

d

c

From Setubal/Meidanis book

Complication - repeated regions Repeated regions: sequences that appears more than once in the molecule. The

copies of repeats do not need to be exactly the same. Problems are illustrated below:

From Setubal/Meidanis book

Coverage and linkage •  coverage = number of times given position is

included in a an aligned fragment. •  if a coverage equals 0 at some column – we do not

have continuous layout. •  linkage amount of overlaps between fragments:

From Setubal/Meidanis book

Complication – lack of coverage

•  Coverage at position i of the target is the number of fragments that cover this position.

•  A conting – continuously covered region.

Target DNA uncovered area

Closing gaps •  sequence walking (direct sequencing)

-  derive a primer from a sequence near the end of a conting -  replicate the sequence starting at the primer -  sequence this the replicated sequence -  if the replicated sequence did not cover the gap, repeat the above steps. - Problems: tedious for larger gap, region of interest must be unique in the genome

• dual end sequencing. Recall that the inserts are much longer than the sequenced fragments. If we sequence both ends of the insert, we obtain mate pairs which can be used as follows: if two ends of a mate pair are in two different contigs, we can deduce the orientation and distance between two contings. Scaffold – sequence of contigs where the order and distances between the contigs are approximately known.,

What do we learn form whole genome sequence

•  Using gene finding algorithm we can discover significant portion of genes

•  Understand the structure of a genome •  Understand genome evolution •  Searching for genes associated with

diseases

Genome duplication

•  Gene duplication – widely accepted method for creation of new genes

•  Ohno proposes that whole genome duplication (polyploidization) provides material for new genomes (1970)

•  2R Hypothesis: two rounds of polyploidization followed by gene loss and functional divergence occurred early in vertebrate lineage.

Syntheny blocks

Results filtered to report segments at least 1000bp, at lest 59% identity

NATURE 1 VOL 40S 114 DECEMBER 20001 www.nature.com 801

In comparative genome analysis synteny blocks = regions containing the homologous genes Below: Segmental duplications in the Arabidopsis genome fund using program MUMer.

How many rounds of genome duplication?

•  Two round of genome duplication should lead to occurrences of groups of four synteny blocks

•  Such tree should be then observed in the current genome

•  They should be consistent •  For vertebrates evolution there is

evidence for full genome duplication

A B C D

Whole genome duplications in yeast

Computational Approach •  Find syntheny blocks •  Find overlaps in syntheny blocks •  Use duplicate synteny blocks do define “sister”

regions in S. cerevisiae (145 sister regions covering 88% of the genome)

Some lessons from whole genome alignment of closely related species

Neutral evolution/natural selection •  natural selection: a process by which biological populations are

altered over time, as a result of the propagation of heritable traits that affect the capacity of individual organisms to survive. –  responsible for organisms being adapted to their environment. –  The theory of natural selection was proposed by Charles Darwin and Alfred

Russel Wallace in 1858, though vaguer and more obscure formulations had been arrived at by earlier researchers.

•  neutral theory of evolution (Kimura 1960): –  vast majority of molecular differences are selectively neutral. –  these genome features are neither subject to, nor explicable by, natural

selection. –  most evolutionary change is the result of genetic drift acting on neutral alleles.

Through drift, these new alleles may become more common within the population. They may subsequently decline and disappear, or in rare cases they may become fixed--meaning that the substitution they carry becomes a universal feature of the population or species

•  The neutralist-selectionist debate – which is the prevalent evolutionary force?

Comparative Genome analysis tools

Assume two closely related organisms (closely for this purpose is that probability of a back substitutions A!X!A are unlikely: example muse/rat; human chimpanzee)

KA - #of coding base substitutions that results in amino-acid change

KS - of coding base substitutions that do not results in amino-acid change (synonymous substitution rate)

KA/ KS – measure of evolutionary constraints KA/ KS << 1; strong purifying selection KA/ KS > 1; possible adaptive or positive selection

KA / K S ratio

Comparison mouse/rat human/chimpanzee Initial sequence of the chimpanzee genome and comparison with Human

genome, The Chimpanzee Genome Sequencing and Analysis Consortium, Nature, August 2005

KA/ KS human-chimpanzee = 0.20 KA/ KS mouse – rat = 0.13 Difference attributed to relaxed evolutionary constrains 4.4% human-chimpanzee orthologs have KA/ KS >1 and are hypothesized to be under positive selection (e.g.. genes involving reproduction)

Same species comparison

•  HapMap project: a multi-country effort to identify and catalog genetic similarities and differences in human beings.

•  In the initial phase of the Project, genetic data are being gathered from four populations with African, Asian, and European ancestry.

•  First version 2005; Second version 2007

SNPs •  Single Nucleotide

Polymorphism (SNP): a variation is a single nucleotide in a genome

•  Typically we have two say alleles (here C and T) minor (less common) and major.

•  minor allele frequency - the ratio of chromosomes in the population carrying the less common variant to those with the more common variant

•  A second generation human haplotype map has over 3.1 million SNPs Figure from Wikipedia

Infinite site mutation model (Kimura 1969)

•  Under the infinite sites mutation model (Kimura,. 1969), mutations never occur twice at the same position

•  This is condition is equivalent to the prefect phylogeny

Recombination •  In eukaryotes recombination

commonly occurs during meiosis as chromosomal crossover between paired chromosomes

•  It has been demonstrated that the points of recombination crossover are not uniformly distributed but instead most of recombinations occur in the so called recombination hotspots

•  Recombination hotspots are not well preserved between human and chimpanzees Copy of the original figure by Morgan

(1916)

Discovering recombination events

•  Note infinite mutation site assumption is equivalent to perfect phylogeny.

•  Four gamete test (Hudson,Kaplan 1985):

SNP1 SNP2

0 1

0 0

1 1 0 1

Under infinite site mutation model (perfect phylogeny) there must be a recombination event between these SNPs

Haplotype, genotype, phasing problem •  Haplotype: description of SNP alleles on a chromosome

–  0/1 vector: 0 for major allele, 1 for minor

•  Genotype: description of alleles on both chromosomes –  0/1/2 vector: 0 (1) - both chromosomes contain the major (minor)

allele; 2 - the chromosomes contain different alleles

11100011 01101001 21102021

two haplotypes per individual

genotype

•  Phasing: the problem of assigning haplotypes given genotypes –  Popular program: PHASE

Linkage disequlibrium

•  the non-random association of alleles at two or more loci

haplotype frequencies deviate from the values they would have if the genes at each locus were combined at random.

random

{

Strong disequlibrium – low recombination level

Measuring linkage disequilibrium { {

A a b

B

pAB=3/5 paB =0/5 qB =3/5

pAb =1/5 pab =1/5 qb =2/5

qA =4/5 qa =1/5 1 Haplotype frequency

{

Allele frequency D = pAB – qAqB= 3/5 – (3/5)(4/5)=15/25-12/25=3/25

observed expected This deviation of the observed frequencies from the expected is referred to as the linkage disequilibrium parameter, D, introduced by Robbins (1918) and named by Lewontin and Kojima (1960)

Other measures

D’ = D/Dmax where Dmax= -min{qAqB, qaqb} if D’< 0. Dmax = min{qaqB, qAqb} if otherwise In our example: (3/25)/(3/25)=1 (1 implies at least one of

the possible haplotypes was not observed) Other measure

r2 = D2 / (qAqBqaqb).

Haplotype blocks •  human genome has a haplotype block structure, such that it

can be divided into discrete blocks of limited haplotype diversity (high LD).

•  To carry out a genome-wide association study, researchers use two groups of participants: people with the disease being studied and similar people without the disease.

•  If certain genetic variations (usually represented by SNPs) are found to be significantly more frequent in people with the disease compared to people without disease, the variations are said to be "associated" with the disease.

•  Assoction of SNP with a disease does not necessarily means that this SNP is causative, but rather points to haplotype block that may contain gene of interest.